Small Ball Estimates for Gaussian Processes under Sobolev Type Norms

Wenbo V. Li; Qi Man Shao

doi:10.1023/A:1021675731663

Small Ball Estimates for Gaussian Processes under Sobolev Type Norms

Wenbo V. Li^*, Qi Man Shao

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

18 Citations (Scopus)

Abstract

A sharp small ball estimate under Sobolev type norms is obtained for certain Gaussian processes in general and for fractional Brownian motions in particular. New method using the techniques in large deviation theory is developed for small ball estimates. As an application the Chung's LIL for fractional Brownian motions is given in this setting.

Original language	English
Pages (from-to)	699-720
Number of pages	22
Journal	Journal of Theoretical Probability
Volume	12
Issue number	3
DOIs	https://doi.org/10.1023/A:1021675731663
Publication status	Published - 1999
Externally published	Yes

Keywords

Chung's LIL
Fractional Brownian motion
Gaussian process
Sobolev norm
Wiener process

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10.1023/A:1021675731663

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title = "Small Ball Estimates for Gaussian Processes under Sobolev Type Norms",

abstract = "A sharp small ball estimate under Sobolev type norms is obtained for certain Gaussian processes in general and for fractional Brownian motions in particular. New method using the techniques in large deviation theory is developed for small ball estimates. As an application the Chung's LIL for fractional Brownian motions is given in this setting.",

keywords = "Chung's LIL, Fractional Brownian motion, Gaussian process, Sobolev norm, Wiener process",

author = "Li, \{Wenbo V.\} and Shao, \{Qi Man\}",

year = "1999",

doi = "10.1023/A:1021675731663",

language = "English",

volume = "12",

pages = "699--720",

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T1 - Small Ball Estimates for Gaussian Processes under Sobolev Type Norms

AU - Li, Wenbo V.

AU - Shao, Qi Man

PY - 1999

Y1 - 1999

N2 - A sharp small ball estimate under Sobolev type norms is obtained for certain Gaussian processes in general and for fractional Brownian motions in particular. New method using the techniques in large deviation theory is developed for small ball estimates. As an application the Chung's LIL for fractional Brownian motions is given in this setting.

AB - A sharp small ball estimate under Sobolev type norms is obtained for certain Gaussian processes in general and for fractional Brownian motions in particular. New method using the techniques in large deviation theory is developed for small ball estimates. As an application the Chung's LIL for fractional Brownian motions is given in this setting.

KW - Chung's LIL

KW - Fractional Brownian motion

KW - Gaussian process

KW - Sobolev norm

KW - Wiener process

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000082131300006

U2 - 10.1023/A:1021675731663

DO - 10.1023/A:1021675731663

M3 - Journal Article

SN - 0894-9840

VL - 12

SP - 699

EP - 720

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 3

ER -

Small Ball Estimates for Gaussian Processes under Sobolev Type Norms

Abstract

Keywords

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